The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |
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Side vi
... of a learned gentleman. To which are also added, the Elements of Plane and
Spherical Trigonometry, which are commonly taught after the Elements of Euclid.
o - THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. s o I. vi PREFACE.
... of a learned gentleman. To which are also added, the Elements of Plane and
Spherical Trigonometry, which are commonly taught after the Elements of Euclid.
o - THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. s o I. vi PREFACE.
Side 197
One part of a straight line cannot be in a plane , and another part above it . * If it
be possible , let AB , part of the straight line ABC , be in the plane , and the part
BC above it : and since the straight line AB is in the plane , it can be proс duced
in ...
One part of a straight line cannot be in a plane , and another part above it . * If it
be possible , let AB , part of the straight line ABC , be in the plane , and the part
BC above it : and since the straight line AB is in the plane , it can be proс duced
in ...
Side 205
But the plane passing through ED , GH is the plane BH ; therefore AF is
perpendicular to the plane BH ; therefore , from the given point A , above the
plane BH , the straight life AF is drawn perpendicular to that plane . Which was to
be done .
But the plane passing through ED , GH is the plane BH ; therefore AF is
perpendicular to the plane BH ; therefore , from the given point A , above the
plane BH , the straight life AF is drawn perpendicular to that plane . Which was to
be done .
Side 207
to the plane which passes through DE , EF , and let it meet that plane in G ; and
through G draw GH parallel ( 31. 1. ) to ED , and GK parallel to EF , and because
BG is perpendicular to the plane through DE , EF , it shall make right anE gles ...
to the plane which passes through DE , EF , and let it meet that plane in G ; and
through G draw GH parallel ( 31. 1. ) to ED , and GK parallel to EF , and because
BG is perpendicular to the plane through DE , EF , it shall make right anE gles ...
Side 209
For the same reason , because the two parallel planes GH , KL H A А. are cut by
the plane AXFC , the G common sections AC , XF , are parallel : and because EX
is parallel to BD , a side of the triangle ABD , as AE to EB , so is ( 2. 6. ) AX to XD
...
For the same reason , because the two parallel planes GH , KL H A А. are cut by
the plane AXFC , the G common sections AC , XF , are parallel : and because EX
is parallel to BD , a side of the triangle ABD , as AE to EB , so is ( 2. 6. ) AX to XD
...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |
Vanlige uttrykk og setninger
added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Populære avsnitt
Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 81 - The angles in the same segment of a circle are equal to one another.
Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 22 - ANY two angles of a triangle are together less than two right angles.
Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Side 24 - Any two sides of a triangle are together greater than the third side.
Bibliografisk informasjon
| Tittel | The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |
| Forfattere | Euclid, Robert Simson |
| Utgiver | Desilver, 1829 |
| Original fra | University of Michigan |
| Digitalisert | 11. jun 2007 |
| Lengde | 516 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |